Many conditions have been introduced to weaken the continuity re-quirements for equilibrium existence in games. We introduce a new con-dition, called regularity, that is simple and easy to verify. It is implied both by Reny's better-reply security and Simon and Zame's endogenous sharing rule...

Discontinuous games, such as auctions, may require special tie-breaking rules to guarantee equilibrium existence. The best results available ensure equilibrium existence only in mixed strategy with endogenously defined tie-breaking rules and communication of private information. We show that an...